Genetic analysis in humans depends heavily on complex, sophisticated statistical methods, since humans cannot be manipulated like experimental animals. But methods are not static, and our understanding of their strengths and weaknesses keeps evolving. Past work supported by this grant has not only developed new methods for genetic analysis but has tested and characterized those methods in rigorous theoretical analyses, supplemented by realistic computer simulations. The research focuses on linkage analysis and segregation analysis, two of the major tools available for understanding complex diseases. Problems and complications will be quantified, and new methods to solve these problems will be developed. Results from this project will assist the genetic analysis of common complex diseases with genetic components, such as diabetes. Greater understanding of the genetic contributions to these diseases will lead, in turn, to improved counseling, treatment, and prevention. Three critical problem areas have been identified: I. Power of parametric and nonparametric linkage methods: Rigorously compare statistical properties of competing methods in this controversial area, under simple and complex genetic models. II. Sex differences and linkage analysis: Analyze sex differences (in recombination fraction and penetrance) in non-X-linked traits and how these differences can affect power of a linkage analysis; quantify how imprinting will influence a linkage analysis; develop new methods to overcome any bias. III. Ascertainment: Solve complex, practical problems of ascertainment, which can profoundly affect the results of a segregation analysis; develop and test good approximations for intractable ascertainment problems, particularly in the context of sequential sampling. The project will not be restricted to the problems detailed above but is designed to be flexible and move rapidly to address new problems of pressing importance as they arise during the grant period.